#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int ztrtri_(char *uplo, char *diag, integer *n,
doublecomplex *a, integer *lda, integer *info)
{
/* -- LAPACK routine (version 3.1) --
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
Purpose
=======
ZTRTRI computes the inverse of a complex upper or lower triangular
matrix A.
This is the Level 3 BLAS version of the algorithm.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
DIAG (input) CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the triangular matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of the array A contains
the upper triangular matrix, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of the array A contains
the lower triangular matrix, and the strictly upper
triangular part of A is not referenced. If DIAG = 'U', the
diagonal elements of A are also not referenced and are
assumed to be 1.
On exit, the (triangular) inverse of the original matrix, in
the same storage format.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, A(i,i) is exactly zero. The triangular
matrix is singular and its inverse can not be computed.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static doublecomplex c_b1 = {1.,0.};
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__2 = 2;
/* System generated locals */
address a__1[2];
integer a_dim1, a_offset, i__1, i__2, i__3[2], i__4, i__5;
doublecomplex z__1;
char ch__1[2];
/* Builtin functions
Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
static integer j, jb, nb, nn;
extern logical lsame_(char *, char *);
static logical upper;
extern /* Subroutine */ int ztrmm_(char *, char *, char *, char *,
integer *, integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *),
ztrsm_(char *, char *, char *, char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *), ztrti2_(char *, char *
, integer *, doublecomplex *, integer *, integer *)
, xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static logical nounit;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
nounit = lsame_(diag, "N");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (! nounit && ! lsame_(diag, "U")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZTRTRI", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Check for singularity if non-unit. */
if (nounit) {
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
i__2 = *info + *info * a_dim1;
if (a[i__2].r == 0. && a[i__2].i == 0.) {
return 0;
}
/* L10: */
}
*info = 0;
}
/* Determine the block size for this environment.
Writing concatenation */
i__3[0] = 1, a__1[0] = uplo;
i__3[1] = 1, a__1[1] = diag;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
nb = ilaenv_(&c__1, "ZTRTRI", ch__1, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)2);
if (nb <= 1 || nb >= *n) {
/* Use unblocked code */
ztrti2_(uplo, diag, n, &a[a_offset], lda, info);
} else {
/* Use blocked code */
if (upper) {
/* Compute inverse of upper triangular matrix */
i__1 = *n;
i__2 = nb;
for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Computing MIN */
i__4 = nb, i__5 = *n - j + 1;
jb = min(i__4,i__5);
/* Compute rows 1:j-1 of current block column */
i__4 = j - 1;
ztrmm_("Left", "Upper", "No transpose", diag, &i__4, &jb, &
c_b1, &a[a_offset], lda, &a[j * a_dim1 + 1], lda);
i__4 = j - 1;
z__1.r = -1., z__1.i = -0.;
ztrsm_("Right", "Upper", "No transpose", diag, &i__4, &jb, &
z__1, &a[j + j * a_dim1], lda, &a[j * a_dim1 + 1],
lda);
/* Compute inverse of current diagonal block */
ztrti2_("Upper", diag, &jb, &a[j + j * a_dim1], lda, info);
/* L20: */
}
} else {
/* Compute inverse of lower triangular matrix */
nn = (*n - 1) / nb * nb + 1;
i__2 = -nb;
for (j = nn; i__2 < 0 ? j >= 1 : j <= 1; j += i__2) {
/* Computing MIN */
i__1 = nb, i__4 = *n - j + 1;
jb = min(i__1,i__4);
if (j + jb <= *n) {
/* Compute rows j+jb:n of current block column */
i__1 = *n - j - jb + 1;
ztrmm_("Left", "Lower", "No transpose", diag, &i__1, &jb,
&c_b1, &a[j + jb + (j + jb) * a_dim1], lda, &a[j
+ jb + j * a_dim1], lda);
i__1 = *n - j - jb + 1;
z__1.r = -1., z__1.i = -0.;
ztrsm_("Right", "Lower", "No transpose", diag, &i__1, &jb,
&z__1, &a[j + j * a_dim1], lda, &a[j + jb + j *
a_dim1], lda);
}
/* Compute inverse of current diagonal block */
ztrti2_("Lower", diag, &jb, &a[j + j * a_dim1], lda, info);
/* L30: */
}
}
}
return 0;
/* End of ZTRTRI */
} /* ztrtri_ */